CN104062659A - Sliding spotlight SAR three-dimensional imaging method based on compressed sensing - Google Patents

Abstract

The invention relates to the field of three-dimensional imaging, in particular to a sliding spotlight SAR three-dimensional imaging method based on compressed sensing. The sliding spotlight SAR three-dimensional imaging method based on compressed sensing aims to solve the problems that the imaging area is small and the imaging precision is low in the prior art. The method comprises the steps that firstly, a sliding spotlight SAR echo model is established for airborne radar devices according to original echo signals received by a scene irradiation area; secondly, SAR imaging is carried out on a two-dimensional sliding spotlight of each radar device in the model; thirdly, SAR images, obtained in the second step, of the radar devices form a three-dimensional matrix; fourthly, compressed sensing is carried out on slices of the three-dimensional matrix, and then the process of sliding spotlight SAR three-dimensional imaging based on compressed sensing is completed.

Description

Sliding spotlight SAR three-D imaging method based on compressed sensing

Technical field

The present invention relates to the Sliding spotlight SAR three-D imaging method based on compressed sensing.

Background technology

Tradition SAR is the two-dimensional imaging to three-dimensional scenic, and it is apart from being determined by the distance of target and radar to image space, and imaging results is actually the superposition of all scatterer scattering coefficients with same distance.Therefore, in two-dimensional SAR imaging, exist cylinder symmetry ambiguity, the folded problems such as phenomenon of covering.Two kinds of simultaneously existing classical SAR patterns, exist corresponding problem.Spotlight SAR Imaging precision is high, but imaging region is little; Stripmap SAR imaging region is large, but imaging precision is lower.

Summary of the invention

The present invention will solve the problem that existing technology imaging region is little and imaging precision is low, and the three-D imaging method of the Sliding spotlight SAR based on compressed sensing is provided.

Sliding spotlight SAR three-D imaging method based on compressed sensing is realized according to the following steps:

One, the original echoed signals that airborne radar receives according to scene irradiated site is set up Sliding spotlight SAR echo model;

Two, the two-dimentional Sliding spotlight SAR imaging to the single radar in model;

Three, the SAR image of the multiple radars after step 2 imaging is formed to a three-dimensional matrice;

Four, to three-dimensional matrice, compressed sensing processing is carried out in section, has completed the Sliding spotlight SAR three-D imaging method based on compressed sensing.

Invention effect:

1, Sliding spotlight SAR imaging model is analyzed

Slip SAR is a kind of SAR imaging pattern of novelty, it by control irradiated site increase the time of orientation to coherent accumulation in the speed of ground moving, thereby improve SAR orientation to resolution.Slip bunching type SAR antenna direction changes between stripmap SAR and Spotlight SAR Imaging between the two, and the position that antenna beam center is pointed to all the time will be distal to the position of imaging scene center, can be regarded as underground certain virtual point of sensing.

2, the Sliding spotlight SAR three-dimensional imaging algorithm based on compressed sensing

2.1 Sliding spotlight SAR imaging algorithms

Slip bunching type SAR is developed according to new mission requirements by stripmap SAR and bunching type SAR, and its imaging algorithm is also planted in the imaging algorithm under these two kinds of SAR patterns.

Utilize a kind of Chirp Scaling algorithm to solve Sliding spotlight SAR imaging problem, as the accurate and efficient algorithm of one, being of wide application of this algorithm, for the RCMC problem in synthetic-aperture radar, by the frequency of Chirp signal is modulated, utilize the mode of phase multiplication to replace interpolation operation when RCMC is revised.Can be to large aperture, and exist the system signal of certain stravismus problem to process, the processing of the beam bunching mode SAR signal that is applicable to slide.

2.2 SAR image elevation imaging algorithms based on compressed sensing

Compressed sensing, as a kind of emerging technology in recent years, has been used to various fields.After the SAR image forming in the array element that obtains space uniform distribution, utilize compressed sensing technology, calculate the elevation information of target, thereby realize three-dimensional imaging.

Utilize the imaging algorithm under Sliding spotlight SAR pattern, obtain under degree of precision, the SAR image in larger region, and utilize compressed sensing algorithm, obtain the elevation information of image.

Brief description of the drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is Sliding spotlight SAR model space geometric;

Fig. 3 is Sliding spotlight SAR tapered plane model;

Fig. 4 is slip pack CS algorithm flow chart;

Fig. 5 is array element spatial distribution model;

Fig. 6 is Sliding spotlight SAR two-dimensional imaging in emulation experiment;

Fig. 7 is compressed sensing elevation imaging in emulation experiment.

Embodiment

Embodiment one: the Sliding spotlight SAR three-D imaging method based on compressed sensing of present embodiment is realized according to the following steps:

One, the original echoed signals that airborne radar receives according to scene irradiated site is set up Sliding spotlight SAR echo model;

Two, the two-dimentional Sliding spotlight SAR imaging to the single radar in model;

Three, the SAR image of the multiple radars after step 2 imaging is formed to a three-dimensional matrice;

Four, to three-dimensional matrice, compressed sensing processing is carried out in section, has completed the Sliding spotlight SAR three-D imaging method based on compressed sensing.

Embodiment two: present embodiment is different from embodiment one: the Sliding spotlight SAR echo model of setting up in described step 1 is specially:

$\begin{array}{c}S(s,\mathrm{\τ})=A_0\·\mathrm{rect}\left[\frac{X-(V_g/V_a)s}{L_s}\right]\·\mathrm{rect}\left[\frac{\mathrm{\τ}-2R\left(s\right)/c}{T_r}\right]\\ \·\exp \{-\mathrm{j\π}{K}_r{\left[\frac{\mathrm{\τ}-2R\left(s\right)/c}{T_r}\right]}^2\}\·\exp \{-j\frac{4\mathrm{\πR}\left(s\right)}{\mathrm{\λ}}\}\end{array}---(1-1)$

Formula represents that aircraft flight arrives (x, 0) and locate the target echo in moment;

Wherein initial point (0,0) is the flight track nearest position of scene center of boarding a plane, R ₀for the flight track nearest distance of scene center of boarding a plane, aircraft is along the operation of x direction of principal axis, and wherein, described vector is defined as x axle, and when initial, aircraft antenna beam center points to (X ₀, R ₀), in the time that aircraft flight is located to (x, 0), beam center points to (X, R ₀), L _sfor wave beam is at ground width, T _rfor pulse width, K _rfor chirp slope, R (s) is the instantaneous distance of aircraft and target, and λ is carrier wavelength, A ₀be a constant, V _athe translational speed of aircraft, V _gbeam scanning region translational speed on the ground, s, τ represent respectively orientation to distance to sampling instant, c is the light velocity, j represents plural number.

Fig. 2 is known, and in present embodiment, pack and band pattern can be regarded the special case of slip beam bunching mode as seen from the figure; In the time that irradiated site translational speed is on the ground zero, be spotlight imaging pattern; In the time of speed that irradiated site is aircraft in the speed of ground moving, be band imaging pattern.When the translational speed of irradiated site zero and air speed between time, with the antenna of same size, because orientation is longer than stripmap SAR to the time of coherent accumulation, therefore its orientation to resolution be greater than the resolution of stripmap SAR.Because the speed that irradiated site in scanning process moves is non-vanishing, so its orientation is larger to imaging size than orientation under beam bunching mode to imaging size.

Other step and parameter are identical with embodiment one.

Embodiment three: present embodiment is different from embodiment one or two: in described step 2, the two dimension of the single radar in model is slided and gathered SAR imaging:

(1) carry out azimuth Fourier transform according to original echoed signals and obtain range-Dopler domain

Original echoed signals is carried out to orientation to Fourier transform, signal domain is changed to range-Dopler domain, according to formula (1-1), the expression formula that obtains the accurate range-Dopler domain of original echoed signals is:

$\begin{array}{c}{S}_{\mathrm{rd}}(f_s,\mathrm{\τ})=C_1\·\exp (-\mathrm{j\π}{K}_s(f_s,R_0)(\mathrm{\τ}-\frac{2}{c}{R}_f{(f_s,R_0)}^2))\\ \·\exp (-j\frac{4\mathrm{\π}{R}_0}{\mathrm{\λ}}{(1-{\left(\frac{\mathrm{\λ}{f}_s}{2V_a}\right)}^2)}^{1/2})\end{array}---(2-1)$

Wherein, C _sthat a coefficient represents the affect f of Doppler frequency on signal trajectory _srepresent that orientation is to frequency, R _fbe illustrated in the range migration in range-Dopler domain, K _sfor equivalent FM slope;

R _f(f _s,R ₀)＝R ₀(1+C _s(f _s)) (2-2)

$C_s\left(f_s\right)=\frac{1}{\sqrt{1-\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}}-1---(2-3)$

$K_s(f_s,R_0)=\frac{K_r}{1-K_r{R}_0\frac{2\mathrm{\λ}}{c^2}\frac{{\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}^2}{{(1-{\left(\frac{{\mathrm{\λf}}_s}{{2V}_a}\right)}^2)}^{3/2}}}---(2-4);$

(2) Chirp Scaling that Doppler domain completes in complementary RCMC proofreaies and correct to adopt first step phase multiplication to adjust the distance, and converts the signal into two-dimensional frequency

The phase function of first step phase multiplication is:

$H_1(f_s,\mathrm{\τ})=\exp \{-\mathrm{j\π}{K}_s(f_s,R_0)\·C_s\left(f_s\right)\·\mathrm{\τ}-\widehat{\mathrm{\τ}}{\left(f_s\right)}^2\}---(2-5)$

Wherein

$\widehat{\mathrm{\τ}}\left(f_s\right)=\frac{2}{c}{R}_0(1+C_s(f_s,R_0))---(2-6)$

for the relative echo time;

Complete complementary RCMC and proofread and correct, carry out afterwards distance to Fourier transform, to adjust the distance to signal to processing, now signal transforms to two-dimensional frequency, and after conversion, signal is:

$\begin{array}{c}S(f_s,f_{\mathrm{\τ}})=C_2\·\exp \{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_0{(1-{\left(\frac{\mathrm{\λ}{f}_s}{2V_a}\right)}^2)}^{1/2}\}\·\exp \left\{\mathrm{j\π}\frac{f_{\mathrm{\τ}}^2}{K_s(f_s,R_0)(1+C_s\left(f_a\right))}\right\}\\ \·\exp \{-j\frac{4\mathrm{\π}}{c}{f}_{\mathrm{\τ}}{R}_0\}\·\exp \{-j\frac{4\mathrm{\π}}{c}{f}_{\mathrm{\τ}}{R}_0{C}_s\left(f_a\right)\}\end{array}---(2-7)$

Wherein, C ₂for constant f _srepresent that orientation is to frequency;

Wherein, first phase term and the R of formula (2-7) ₀relevant, he represents that orientation is to frequency modulation (PFM), irrelevant to compression with ensuing distance.Have second in formula (2-7), four exponential terms to distance to relevant, ensuing second step phase multiplication exactly in order to compensate second, four exponential terms, thereby realize Range compress, exp{} represents phase place;

(3) adopt second step phase multiplication to complete Range compress, secondary range compression is proofreaied and correct with complementary RCMC, by distance to pulse signal boil down to distance to a point

The phase function of second step phase multiplication is:

$H_2(f_s,f_{\mathrm{\τ}})=\exp \{-\mathrm{j\π}\frac{f_{\mathrm{\τ}}^2}{K_s(f_s,R_0)(1+C_S\left(f_s\right))}\}\exp \left\{j\frac{4\mathrm{\π}{f}_{\mathrm{\τ}}{R}_0{C}_s\left(f_s\right)}{c}\right\}---(2-8)$

Signal after treatment is carried out to orientation to Fourier inversion

After phase multiplication, adjust the distance and complete to the processing of signal for the second time, the range-Dopler domain of signal need to being remapped, to carry out last orientation to compression to signal.So carry out distance to Fourier inversion.

(4) adopt the 3rd step phase multiplication to complete Azimuth Compression and phase correction

At range-Dopler domain to orientation to carrying out orientation to compression, its essence is target is corrected to zero doppler position, thereby realize in orientation to by point of the echoed signal boil down to of target.

$H_3(f_s,\mathrm{\τ})=\exp \{-j\frac{4\mathrm{\π}{R}_0}{\mathrm{\λ}}{(1-{\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}^2)}^{1/2}\}---(2-9)$

So far, the processing in echoed signal orientation is all completed, signal need to be changed to SAR image area again, thus to signal carry out orientation to inverse Fourier transform, signal returns to SAR image area, output image.

Other step and parameter are identical with embodiment one or two.

Embodiment four: present embodiment is different from one of embodiment one to three: described step 3 is specially:

Utilize the two-dimentional Sliding spotlight SAR imaging algorithm of the single radar of step 2, establishing the SAR image that i radar obtain is Sar _i(s, τ), the three-dimensional matrice that utilizes multiple radars to form is

SAR(s,τ,i)＝Sar _i(s,τ)。

Other step and parameter are identical with one of embodiment one to three.

Embodiment five: present embodiment is different from one of embodiment one to four: described step 4 is specially:

The principle of high computational is the difference of the echo delay that receives of the radar that distributes by three-dimensional matrice space uniform, utilizes l ₁norm compressed sensing is tried to achieve object height;

Build the sparse base of elevation matrix according to radar three-dimensional space of matrices distributed model

$\mathrm{\Φ}(i,j)=\exp \{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}(R_0+\frac{{(D\left(i\right)-h\left(j\right))}^2}{{2R}_0})\}---(2-10)$

The elevation that wherein D (i) is array element is to distribution, and the array element that space uniform distributes is spaced apart d, and N is array element sum;

$D\left(i\right)=(i-[\frac{N}{2}\left]\right)\·d---(2-11)$

The elevation that h (j) is reconstruction signal is to distribution, and the image that the radar that three-dimensional matrice space uniform is distributed obtains is cut into slices, and then to carry out protruding optimization be l to the pixel of the image same position to equally distributed radar ₁norm compressed sensing obtains the elevation information that this pixel position is corresponding.

Other step and parameter are identical with one of embodiment one to four.

Emulation experiment:

One, the scene simulation of the SAR elevation imaging based on compressed sensing

The setting of table 1 radar parameter

A target is set at scanning area center, and target is 50m with respect to the vertical height of array element center and scanning center's line, 10 array elements is set target is carried out to scanning imagery, the base length d=20m between the array element that space uniform distributes.

Two, simulation result and analysis

Can obtain by emulation the SAR image that each array element obtains by slip beam bunching mode, with center array element for for example descending Fig. 6;

Can find out that imaging results is realistic, target in orientation to center, the imaging results of array element that space uniform is distributed cut into slices (extracting the data that each array element target is expert at) carry out the imaging of compressed sensing elevation and obtain following Fig. 7 of elevation result of target:

As seen from Figure 7 point target calculate to elevation information be 50m, conform to actual conditions, compressed sensing algorithm can obtain the elevation information of target accurately, thereby realizes Sliding spotlight SAR three-dimensional imaging.Can reach a conclusion thus: the Sliding spotlight SAR three-dimensional imaging algorithm based on compressed sensing can obtain under degree of precision, SAR image and the elevation information thereof in larger region.

Claims (5)

1. the Sliding spotlight SAR three-D imaging method based on compressed sensing, is characterized in that the Sliding spotlight SAR three-D imaging method based on compressed sensing is realized according to the following steps:

One, the original echoed signals that airborne radar receives according to scene irradiated site is set up Sliding spotlight SAR echo model;

Two, the two-dimentional Sliding spotlight SAR imaging to the single radar in model;

Three, the SAR image of the multiple radars after step 2 imaging is formed to a three-dimensional matrice;

Four, to three-dimensional matrice, compressed sensing processing is carried out in section, has completed the Sliding spotlight SAR three-D imaging method based on compressed sensing.

2. the Sliding spotlight SAR three-D imaging method based on compressed sensing according to claim 1, is characterized in that the Sliding spotlight SAR echo model of setting up in described step 1 is specially:

$\begin{array}{c}S(s,\mathrm{\τ})=A_0\·\mathrm{rect}\left[\frac{X-(V_g/V_a)s}{L_s}\right]\·\mathrm{rect}\left[\frac{\mathrm{\τ}-2R\left(s\right)/c}{T_r}\right]\\ \·\exp \{-\mathrm{j\π}{K}_r{\left[\frac{\mathrm{\τ}-2R\left(s\right)/c}{T_r}\right]}^2\}\·\exp \{-j\frac{4\mathrm{\πR}\left(s\right)}{\mathrm{\λ}}\}\end{array}---(1-1)$

Formula represents that aircraft flight arrives (x, 0) and locate the target echo in moment;

Wherein initial point (0,0) is the flight track nearest position of scene center of boarding a plane, R ₀for the flight track nearest distance of scene center of boarding a plane, aircraft is along the operation of x direction of principal axis, and wherein, described vector is defined as x axle, and when initial, aircraft antenna beam center points to (X ₀, R ₀), in the time that aircraft flight is located to (x, 0), beam center points to (X, R ₀), L _sfor wave beam is at ground width, T _rfor pulse width, K _rfor chirp slope, R (s) is the instantaneous distance of aircraft and target, and λ is carrier wavelength, A ₀be a constant, V _athe translational speed of aircraft, V _gbeam scanning region translational speed on the ground, s, τ represent respectively orientation to distance to sampling instant, c is the light velocity, j represents plural number.

3. the Sliding spotlight SAR three-D imaging method based on compressed sensing according to claim 2, is characterized in that the two-dimentional Sliding spotlight SAR imaging to the single radar in model in described step 2:

(1), carry out azimuth Fourier transform according to the original echoed signals of SAR signal domain and obtain range-Dopler domain

Original echoed signals is carried out to orientation to Fourier transform, SAR signal domain is changed to range-Dopler domain, according to formula (1-1), the expression formula that obtains the accurate range-Dopler domain of original echoed signals is:

$\begin{array}{c}{S}_{\mathrm{rd}}(f_s,\mathrm{\τ})=C_1\·\exp (-\mathrm{j\π}{K}_s(f_s,R_0)(\mathrm{\τ}-\frac{2}{c}{R}_f{(f_s,R_0)}^2))\\ \·\exp (-j\frac{4\mathrm{\π}{R}_0}{\mathrm{\λ}}{(1-{\left(\frac{\mathrm{\λ}{f}_s}{2V_a}\right)}^2)}^{1/2})\end{array}---(2-1)$

Wherein, C _sthat a coefficient represents the impact of Doppler frequency on signal trajectory, f _srepresent that orientation is to frequency, R _fbe illustrated in the range migration in range-Dopler domain, K _sfor equivalent FM slope;

R _f(f _s,R ₀)＝R ₀(1+C _s(f _s)) (2-2)

$C_s\left(f_s\right)=\frac{1}{\sqrt{1-\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}}-1---(2-3)$

$K_s(f_s,R_0)=\frac{K_r}{1-K_r{R}_0\frac{2\mathrm{\λ}}{c^2}\frac{{\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}^2}{{(1-{\left(\frac{{\mathrm{\λf}}_s}{{2V}_a}\right)}^2)}^{3/2}}}---(2-4);$

(2) Chirp Scaling that Doppler domain completes in complementary RCMC proofreaies and correct to adopt first step phase multiplication to adjust the distance, and converts the signal into two-dimensional frequency

The phase function of first step phase multiplication is:

$H_1(f_s,\mathrm{\τ})=\exp \{-\mathrm{j\π}{K}_s(f_s,R_0)\·C_s\left(f_s\right)\·\mathrm{\τ}-\widehat{\mathrm{\τ}}{\left(f_s\right)}^2\}---(2-5)$

Wherein for the relative echo time;

$\widehat{\mathrm{\τ}}\left(f_s\right)=\frac{2}{c}{R}_0(1+C_s(f_s,R_0))---(2-6)$

The Doppler domain signal of adjusting the distance carries out distance to Fourier transform, and signal transforms to two-dimensional frequency, conversion after signal be distance to pulse signal:

$\begin{array}{c}S(f_s,f_{\mathrm{\τ}})=C_2\·\exp \{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}{R}_0{(1-{\left(\frac{\mathrm{\λ}{f}_s}{2V_a}\right)}^2)}^{1/2}\}\·\exp \left\{\mathrm{j\π}\frac{f_{\mathrm{\τ}}^2}{K_s(f_s,R_0)(1+C_s\left(f_a\right))}\right\}\\ \·\exp \{-j\frac{4\mathrm{\π}}{c}{f}_{\mathrm{\τ}}{R}_0\}\·\exp \{-j\frac{4\mathrm{\π}}{c}{f}_{\mathrm{\τ}}{R}_0{C}_s\left(f_a\right)\}\end{array}---(2-7)$

Wherein, C ₂for constant, f _srepresent that orientation is to frequency;

(3) adopt second step phase multiplication to complete Range compress, secondary range compression is proofreaied and correct with complementary RCMC, by distance to pulse signal boil down to distance to a point

The phase function of second step phase multiplication is:

$H_2(f_s,f_{\mathrm{\τ}})=\exp \{-\mathrm{j\π}\frac{f_{\mathrm{\τ}}^2}{K_s(f_s,R_0)(1+C_S\left(f_s\right))}\}\exp \left\{j\frac{4\mathrm{\π}{f}_{\mathrm{\τ}}{R}_0{C}_s\left(f_s\right)}{c}\right\}---(2-8)$

Adjust the distance to pulse signal carry out orientation to Fourier inversion, obtain a point of range-Dopler domain;

(4) adopt the 3rd step phase multiplication to complete Azimuth Compression and phase correction

At range-Dopler domain to orientation to carrying out orientation to compression, then target is corrected to zero doppler position, in orientation to by point of the echoed signal boil down to of target;

The phase function of the 3rd step phase multiplication is:

$H_3(f_s,\mathrm{\τ})=\exp \{-j\frac{4\mathrm{\π}{R}_0}{\mathrm{\λ}}{(1-{\left(\frac{\mathrm{\λ}{f}_s}{{2V}_a}\right)}^2)}^{1/2}\}---(2-9)$

To signal carry out orientation to inverse Fourier transform, signal returns to SAR image area, output image.

4. the Sliding spotlight SAR three-D imaging method based on compressed sensing according to claim 3, is characterized in that described step 3 is specially:

Utilize the two-dimentional Sliding spotlight SAR imaging algorithm of the single radar of step 2, establishing the SAR image that i radar obtain is Sar _i(s, τ), the three-dimensional matrice that utilizes multiple radars to form is

SAR(s,τ,i)＝Sar _i(s,τ)。

5. the Sliding spotlight SAR three-D imaging method based on compressed sensing according to claim 4, is characterized in that described step 4 is specially:

The principle of high computational is the difference of the echo delay that receives of the radar that distributes by three-dimensional matrice space uniform, utilizes l ₁norm compressed sensing is tried to achieve object height;

Build the sparse base of elevation matrix according to radar three-dimensional space of matrices distributed model

$\mathrm{\Φ}(i,j)=\exp \{-j\frac{4\mathrm{\π}}{\mathrm{\λ}}(R_0+\frac{{(D\left(i\right)-h\left(j\right))}^2}{{2R}_0})\}---(2-10)$

The elevation that wherein D (i) is array element is to distribution, and the array element that space uniform distributes is spaced apart d, and N is array element sum;

$D\left(i\right)=(i-[\frac{N}{2}\left]\right)\·d---(2-11)$

The elevation that h (j) is reconstruction signal is to distribution, and the image that the radar that three-dimensional matrice space uniform is distributed obtains is cut into slices, and then to carry out protruding optimization be l to the pixel of the image same position to equally distributed radar ₁norm compressed sensing obtains the elevation information that this pixel position is corresponding.